On the Equivalence of Graph Cuts and Max-product Belief Propagation
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If you have a question about this talk, please contact Peter Orbanz.
(Joint work with Inmar Givoni, Richard Zemel, and Brendan Frey.)
A common task in computer vision is the minimization of pairwise
submodular energies over binary
variables. For such problems, both graph cuts and max-product belief
propagation are applicable.
Graph cuts is guaranteed to produce optimal solutions, and empirically
it does so very quickly.
Max-product can be applied in more general settings, but it is not
guaranteed to be optimal even in
the binary submodular case, and empirically it has been shown to
produce suboptimal results while
taking longer to do so.
Both algorithms operate on parametric representations of an underlying
energy function, and it is
known that both algorithms can be viewed as performing iterative
reparameterizations of that energy
function. This suggests that despite the difference in empirical
performance, under a certain view,
the two algorithms might be similar.
In this talk, I will present graph cuts and max-product via this lense
of reparameterization, then I
will develop the precise connection between the algorithms, showing
that with proper scheduling and
damping, max-product can be made equivalent to graph cuts. The end
result is a scheduling algorithm
and damping procedure for max-product that is guaranteed to be
efficient and optimal on binary
submodular problems, even when the graphical model has loopy structure.
This talk is part of the Machine Learning @ CUED series.
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